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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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2018 Impact Factor: 0.565

Front. Math. China    2023, Vol. 18 Issue (1) : 1-14    https://doi.org/10.3868/S140-DDD-023-005-X
SURVEY ARTICLE
Alternating link and its generalization
Liangxia WAN()
School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
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Abstract

The alternating links give a classical class of links. They play an important role in Knot Theory. Ozsváth and Szabó introduced a quasi-alternating link which is a generalization of an alternating link. In this paper we review some results of alternating links and quasi-alternating links on the Jones polynomial and the Khovanov homology. Moreover, we introduce a long pass link. Several problems worthy of further study are provided.

Keywords Alternating links      quasi-alternating links      pass replacement      Jones polynomial      Khovanov homology     
Online First Date: 22 May 2023    Issue Date: 31 May 2023
 Cite this article:   
Liangxia WAN. Alternating link and its generalization[J]. Front. Math. China, 2023, 18(1): 1-14.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.3868/S140-DDD-023-005-X
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I1/1
Fig.1  Reidemeister movers
Fig.2  Two revolutions
Fig.3  Thistlethwaite KT
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